OPTIMALITY THEORY: MOTIVATIONS AND PERSPECTIVES Pavel Iosad 1 THE BASICS OF OT The classic version of Optimality Theory, first described in detail by Prince & Smolensky (1993), is a phonological framework that privileges the simultaneous satisfaction of multiple, violable constraints by phonological representations over the gradual construction of correct representations from given inputs. At its core, an OT grammar implements a search procedure that finds the surface form that is most compatible with the relevant underlying representation, given the specific properties of the particular language. In OT, these language-specific properties are encoded as a series of rankable, violable constraints. 1.1 Constraints: CON In formal terms, a constraint is most commonly understood as a function that maps from an ⟨input, output⟩ pair to an integer corresponding to the number of violations incurred by that pair. In practice, constraints are most commonly formulated as imperative statements of the form “Assign a violation mark [i.e., increment the return value of the function by 1] for each instance in ⟨input, output⟩ of a structure characterized by some property X”. Thus, a constraints against postvocalic stops, 1 which in OT parlance could be written as *V[−son −cont], would penalize any substrings of an output candidate that contain a vowel, followed by a stop. A form like [tata], therefore, incurs one violation of the constraint; a form like [tapata] incurs two; and forms like [tat] and [saθa] incur zero: in the former case since no stop in the form is postvocalic, and in the latter case since there are no stops in the form at all.1 In standard OT, constraints come in two varieties: markedness and faithfulness constraints. As discussed by Moreton (2004), markedness constraints are distinguished by the fact the number of violations they assign does not depend on the properties of the input in the ⟨input, output⟩ pair. The constraint *V[−son −cont] is an example: it only refers to properties of the output, and always assigns the same number of violation marks (zero) to a candidate with output [taθa], irrespective of whether the input is [tata] or [taθa]. Markedness constraints, therefore, are statements about the preferred shape of surface representations. Faithfulness constraints, on the other hand, demand that certain aspects of the input should be preserved in the output. Formally, a faithfulness constraint never assigns a violation mark to the fully faithful candidate: a constraint � is a faithfulness constraint if there are no ⟨input, output⟩ pairs such that the input is identical to that output and � assigns a violation mark to the pair. A common type of faithfulness constraint, for example, demands that input and output be identical in the value of some distinctive feature. A constraint like IDENT-IO([±continuant]) will therefore assign one violation mark to an input-output pair ⟨/tata/, [taθa]⟩ (since the highlighted segment changes its value of [±continuant]) but none to ⟨/tata/, [tata]⟩. 2 1.2 The candidates: GEN The set of potential output forms, produced by the module GEN, is, in classic OT, assumed to be both infinite and independent of the properties of the input. The only restriction on GEN admitted in classic theory is the extent of “the basic structural resources of the representational theory” (Prince & Smolensky 1993: 6): in other words, GEN makes available, as potentially corresponding to any input, any phonological object that does not violate the tenets of representational theory. This independence of outputs from inputs severely restricts the analyst’s freedom to account for phonological phenomena in ways other than constraint (re)ranking. If some output is ungrammatical in a language (for a particular input), this cannot be — in classic OT — accounted for by assuming that this derives from some input property that restricts the range of potential outputs. The explanatory burden is thus shifted from restrictions on the set of forms to be considered to the evaluation procedure, described in the next section. 1.3 The evaluation procedure: EVAL The fundamental concept of OT is constraint ranking. All the constraints are arranged in a relation of dominance, which is transitive: in each pair of constraints either one outranks the other or they are unranked with respect to each other, and if A ≫ B and B ≫ C then necessarily A ≫ C. The concept of ranking comes into play in the EVAL module, which chooses the correct output from the candidate set offered by the universal mechanism GEN. 3 In a nutshell, EVAL chooses the candidate that has the fewest violations of the highest- ranked constraint. In practice, one constraint is rarely enough to select the “winner”, so the procedure is commonly described recursively. For each constraint and a pair of candidates, it is possible to determine if the constraint favours one of the candidates: the favoured candidate accrues fewer violations than the disfavoured one. Once the constraints are arranged in ranking order, the candidate set is winnowed by rejecting all candidates that are disfavoured by the highest-ranked constraint, in the sense that there exist other candidates that accrue fewer violations of that constraint. In classic OT, once a candidate is excluded from consideration by some constraint, it can never be a winner (domination is strict) — but see Krämer (this volume) for discussion of other alternatives. Those candidates that survive this procedure are passed on to the next constraint in the ranking, and the winnowing is repeated until either the bottom of the ranking is reached or there is only one candidate left. This interplay of markedness and faithfulness has an important consequence for the scope of the theory. In OT, the concept of a phonological rule — a mechanism that rewrites part of an input string — is largely replaced by that of the unfaithful mapping, whereby the winning candidate is not identical to the input in one respect or another. Unfaithful mappings necessarily violate faithfulness constraints: therefore, they can only be allowed when the relevant faithfulness constraints are outranked by some markedness constraints. This is the basic markedness-over-faithfulnes (M ≫ F) schema. Consider the example of gorgia toscana: a process in Tuscan varieties of Italian whereby stops become fricatives in intervocalic positions (Giannelli & Savoia 1978; 1980; Giannelli & Cravens 1996; Kirchner 2000).2 In isolation, input /kasa/ for ‘home’ is realized as [ˈkaːsa], whereas in a phrasal context after a vowel the initial 4 stop becomes a continuant, often [h]: [la ˈhaːsa] ‘the home’. Ignoring for now the assignment of prosodic structure (specifically stress assignment and vowel lengthening) and /s/-voicing, the crucial mapping is /k/ → [h]. This mapping violates a faithfulness constraint that demands the preservation of [±cont] values (IDENT[±cont]). In the citation form, this constraint remains unviolated, but in the postvocalic context it cannot prevent the unfaithful mapping. Thus, for instance, IDENT[±cont] outranks the constraint *[−son −cont] that militates against surface stop consonants: in other words, it is more important to avoid changes in continuancy (e.g. spirantization) than to avoid the presence of stops in the output. In OT work, this is formalized as in (1). (1) Faithfulness over markedness /kasa/ IDENT[±cont] *[−son −cont] a. ☞ [kasa] * b. [xasa] *! The diagram in (1), referred to in OT parlance as a tableau, demonstrates the derivation of [kasa] from /kasa/. Candidate (a.), which eventually wins, is favoured by IDENT over candidate (b.), where the [cont] value of the [k] is changed, acquiring one violation of the faithfulness constraint (marked by the asterisk). Since the fully faithful candidate (a.) is favoured by the IDENT constraint, candidate (b.) is knocked out of contention (as the exclamation mark indicates). Although the favouring relationship is reversed for the constraint [−son −cont], that constraint is ranked too low, i.e. below the IDENT constraint, to force the choice of candidate (b.) 5 When the input puts the stop in a postvocalic position, the mapping effected is unfaithful. This must be due to a different markedness constraint, militating against postvocalic stops. This constraint outranks the IDENT constraint. (2) Markedness over faithfulness *V[−son −cont] IDENT[±cont] *[−son −cont] /kasa/ a. ☞ [kasa] * b. [xasa] *! /la kasa/ c. [la kasa] *! * d. ☞ [la hasa] * In the case of the input /kasa/, neither candidate violates the contextually determined markedness constraint, since neither contains the offending sequence of a vowel and a stop (in these case the constraint is sometimes said to be vacuously satisfied). The evaluation is passed on to the next constraint — IDENT — with the same results as in (1). As for /la kasa/, the constraint against postvocalic stops knocks out the faithful candidate and an unfaithful mapping ensues. It is important to note a non-trivial shift in emphasis compared to rule-based phonology. There is no real analogue to a “faithful mapping” in a rule-based theory: if an output happens to be identical to its input, this is an epiphenomenon of the fact that no rule happens to apply to it, and it does not require a special account. In OT, a faithful mapping requires an explanation just as much as an unfaithful one: it becomes a phonological fact. In fact, the faithfulness of mappings plays a important role in 6 much of the work on learnability (Tesar 2013), which is likely to have been facilitated by the fact that it can be expressed formally within the theory. However, not all phenomena of interest to the phonologist boil down to unfaithful mappings. A notable class of cases includes structure-building operations such as the construction of prosodic structure. The classic example is syllabification, which is commonly assumed to be driven solely by the interaction of several markedness constraints, such as ONSET (penalizing onsetless syllables) and NOCODA (penalizing codas). Faithfulness to syllable structure does not come into the picture: this is catered for by an assumption that faithfulness constraints to syllabic structure are not part of CON.